Blow-up Solutions for General Toda Systems on Riemann Surfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911511005364224 |
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| author | Hu, Zhengni Zhu, Miaomiao |
| author_facet | Hu, Zhengni Zhu, Miaomiao |
| contents | In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular perturbation methods, where the concentration rates of different components occur in distinct orders. In particular, we establish the existence of asymmetric blow-up solutions for the $SU(3)$ Toda system. Furthermore, the blow-up points are precisely located at the ``$k$-symmetric'' centers of the surface.
Keywords: Toda system, Neumann boundary condition, Blow-up solutions, $k$-symmetry, Finite-dimensional reduction |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04777 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-up Solutions for General Toda Systems on Riemann Surfaces Hu, Zhengni Zhu, Miaomiao Analysis of PDEs Primary: 35J20 35J57, Secondary: 35J61 In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular perturbation methods, where the concentration rates of different components occur in distinct orders. In particular, we establish the existence of asymmetric blow-up solutions for the $SU(3)$ Toda system. Furthermore, the blow-up points are precisely located at the ``$k$-symmetric'' centers of the surface. Keywords: Toda system, Neumann boundary condition, Blow-up solutions, $k$-symmetry, Finite-dimensional reduction |
| title | Blow-up Solutions for General Toda Systems on Riemann Surfaces |
| topic | Analysis of PDEs Primary: 35J20 35J57, Secondary: 35J61 |
| url | https://arxiv.org/abs/2602.04777 |